A mathematical formula reveals the secret to lasting relationships

If you're fortunate enough to
find someone you want to settle down with forever, the next
question is: How do you achieve happily ever after?

According to mathematician
Hannah Fry, it may come down to a simple formula.

Fry, who works at the UCL
Centre for Advanced Spatial Analysis in London, explains in her
2014
TED Talk and recently released book, "The
Mathematics of Love," that the best predictor of long-lasting
relationships is how positive and negative a couple can be to one
another.

In her book, she discusses
the groundbreaking work of psychologist John Gottman and his
team. Over many years they observed hundreds of couples and noted
their facial expressions, heart rates, blood pressure, skin
conductivity, and the words they used in conversation with their
partners.

They discovered low-risk
couples have more positive interactions with each other, and
high-risk couples tend to spiral into negativity.

As Fry puts it, "In
relationships where both partners consider themselves as happy,
bad behavior is dismissed as unusual." For example, a wife might
assume her husband's grumpiness is due to stress at work or a bad
night's sleep.

"In negative relationships, however, the situation is reversed,"
writes Fry. "Bad behavior is considered the norm." A husband, for
instance, might think his wife's grumpiness is "typical," due to
her "selfishness" or other negative personality trait.

Gottman then teamed up with mathematician James Murray, and they
began to understand how these spirals of negativity happen. They
came up with the below equations, which predict how positive or
negative a husband and wife will be at the next point in their
conversation.

As Fry explains, the model is framed as husband and wife but also
applies to same-sex spouses and unmarried couples in long-term
relationships.

Gottman and Murray found that the influence a couple has on each
other is the most important factor. If a husband says something
positive, like agrees with his wife or makes a joke, the wife
will likely react positively in turn. Meanwhile, if he does
something negative, like interrupts her or dismisses something
she's said, she will likely be negatively impacted.

The "negativity threshold" pinpoints when the wife becomes so
frustrated by her husband that she responds very negatively.

Interestingly, Fry says she
would have imagined that the best relationships would have a high
negativity threshold, meaning they'd be focused on compromise and
would bring up an issue only if it was "a really big deal." But
in fact, the opposite is true.

"The most successful
relationships are the ones with a really low negativity
threshold," writes Fry. "In those relationships, couples allow
each other to complain, and work together to constantly repair
the tiny issues between them. In such a case, couples don't
bottle up their feelings, and little things don't end up being
blown completely out of proportion."

Happy couples, then, tend to
have more positive interactions than negative ones, and thus are
more likely to give each other the benefit of a doubt. When there
is an issue, they're more likely to bring it up quickly, fix it,
and move on.

"Mathematics leaves us with a
positive message for our relationships," Fry says, "reinforcing
the age-old wisdom that you really shouldn't let the sun go down
on your anger."